Queda acentuada de CORE (CORE)

This article introduces a novel training paradigm for generative models called Explorative Modeling (XM), which enables true end-to-end training. Traditionally, powerful generative models like autoregressive and diffusion models are not trained end-to-end. They are trained to predict a single small step but require iterative multi-step sampling for inference. This "exposure bias" leads to error accumulation and limits performance. The core challenge XM addresses is "mode blurring." In generative tasks, a single input (e.g., "generate a dog") corresponds to many valid outputs (multiple modes). Standard training objectives like reconstruction loss force the model to average these modes, producing unrealistic, blurry outputs. To avoid this, existing models break generation into many small, almost deterministic steps, sacrificing end-to-end training. XM tackles this by restructuring the training loop itself. Its key insight is to amplify "generative expressivity." For each training input, instead of generating one sample, the model generates K candidate outputs. Only the candidate closest to the real data is used for computing the loss and updating the model via backpropagation. This simple "best-of-K" mechanism is implemented as a short for-loop. By exploring multiple possibilities, the model learns to distribute its guesses across different modes rather than collapsing to their uninformative average. The paper demonstrates that "exploration" acts as a new, powerful scaling axis. Gains from XM increase with model size, data scale, and compute. Experiments show improvements in FID scores for image generation and significant efficiency gains, sometimes outperforming larger models without exploration. When pushed to the limit, XM enables fully single-step, end-to-end generative models. In robotics tasks, an "Explorative Policy" matched the performance of a 100-step Diffusion Policy with a single forward pass, drastically improving inference speed. While the best-of-K concept is not entirely new, the authors' contribution lies in formally understanding it as a direct method to boost generative expressivity without fragmenting the generation process. This work suggests that as models scale, enhancing exploration during training may become crucial for overcoming fundamental performance bottlenecks.

Strong corporate earnings are providing robust support for the U.S. equity market. John Flood, a partner at Goldman Sachs, argues that with market positioning becoming "cleaner," the S&P 500 could set a new all-time high this year, driven fundamentally by corporate profits. According to Goldman Sachs data, the S&P 500's trailing second-quarter EPS growth reached 45% year-over-year, significantly surpassing the initial consensus of 22%. Excluding non-recurring items, such as certain investment-related income, the adjusted EPS growth rate remains a strong 26%, accelerating from Q1 and marking the fastest pace since 2021. This strong performance has led analysts to upwardly revise forward earnings estimates for 2027, with positive revisions breadth across most sectors. Concurrently, market sentiment and positioning have cooled from earlier highs. Goldman's sentiment and positioning indicators have retreated, hedge funds have notably reduced leverage, and retail investor leverage is also moderating. Flood views this "de-foaming" of market positioning as creating a healthier foundation for further market gains. From a valuation perspective, U.S. stocks appear relatively inexpensive compared to other major global markets. Furthermore, Flood notes that the primary benefits of the AI super-cycle have yet to fully materialize. However, a seasonal risk is noted: historical data shows muted median returns for the S&P 500 from early August to Election Day in mid-term election years. Goldman's conclusion is that the positive earnings outlook provides strong support for the bullish case, but its sustainability remains a key variable for the market's trajectory.

OpenAI releases a 62-page core manuscript detailing how its AI model independently solved ten major, longstanding mathematical problems considered "Fields Medal-level." The breakthroughs, achieved at an estimated computational cost of only $2,000, include advancing a 46-year-old upper bound for high-dimensional sphere packing and explicitly constructing a non-sofic group—a 27-year-old open question. The manuscript, titled "How the Ideas Came Together," was authored autonomously by the AI (reportedly the next-generation model Astra). It reconstructs the reasoning process for each problem: identifying initial promising paths, obstacles encountered, pivotal shifts in perspective, and the final decisive insights. For sphere packing, the AI moved beyond traditional linear programming limits by employing Mellin transforms and harmonic measure to refine the density exponent. For the non-sofic group, the key was resolving a "crucial mismatch" between having many expansion graphs and needing one, via a controlled median-based function. OpenAI researcher Mo Bavarian reflects on the rapid progress from AI struggling with grade-school math to solving profound mathematical conjectures, calling this moment "more surreal than any before" and akin to the eve of a technological singularity.

Bank of America's Bull & Bear indicator rose to 9.7 in early August, its highest since 2021 and nearing a "sell" signal. Weekly flows showed $52.9B into cash, $32.9B into equities, and $23.1B into bonds. The report highlights a core market contradiction: clear policy intent to backstop financial conditions (evidenced by recent coordinated FX intervention, termed a "poor man's LTCM event") versus extreme bullish sentiment, widening credit spreads for AI mega-cap firms, and rising political uncertainty ahead of the midterm elections. Fund flows were mixed: while equity inflows are on a record annualized pace, the tech sector saw its first outflow in six weeks. Bank of America's strategy advises a "summer retreat or rotation"—exiting risk assets or rotating into defensive sectors (consumer staples), duration assets (REITs, small caps, biotech), and the USD to hedge against potential financial tightening. The midterm election is identified as the key macro variable for H2 2026, acting as a referendum on populist fiscal policies. A Republican-held Senate is viewed as market-positive. The report also notes that AI capital expenditure momentum requires the Mag 7 index to recover above 50 to counter threats from cheap Chinese computing. Near-term market direction may hinge on July payroll data, influencing the Fed's Jackson Hole stance. Overall, while liquidity backstops provide downside protection, the extreme Bull & Bear reading suggests limited upside.

In an astonishing development, a longstanding mathematical problem known as the Crouzeix conjecture, which had challenged experts in numerical linear algebra for 22 years, appears to have been solved by Shanmu Jin, a neurosurgery resident and postdoctoral researcher at Peking Union Medical College Hospital. With no formal advanced mathematical training—his background is in geology and medicine—Jin relied on self-study and, crucially, the AI model GPT-5.6. The conjecture, proposed by mathematician Michel Crouzeix in 2004, concerns a fundamental constant (speculated to be 2) bounding the relationship between matrix norms and polynomial values over numerical ranges. It is critical for applications in matrix function analysis and numerical methods. Despite dedicated efforts by leading mathematicians, the best proven constant had only been reduced to 2.414. Jin approached the problem using sophisticated prompt engineering with GPT-5.6. He adapted a known prompting strategy, isolating the AI from external resources to force original reasoning, employing multiple divergent "sub-agents" to explore different paths, and enforcing rigorous adversarial review of proposed proof steps. After about 16 hours of autonomous, unsupervised operation, the AI produced a novel and elegant proof. The key insight involved a clever "sampling strategy" that reduced the problem to a simple positivity condition—a solution described as elegant and unexpected by experts. The proof was verified by the conjecture's originator, Michel Crouzeix, and other specialists like Alex Townsend and Anne Greenbaum, who expressed astonishment at its validity. Jin has made the entire process open-source, including the prompt, drafts, and formal verification code. Remarkably, just eight days after Jin's preprint appeared, mathematicians Emiel Lorist and Felix Schwenninger published an independent, concise 5-page proof using a different approach, also developed with the aid of ChatGPT 5.6. Jin welcomed this complementary work. This event marks a potential turning point, demonstrating how AI can enable experts from non-traditional backgrounds to solve deep theoretical problems and dramatically accelerate scientific discovery, heralding what some are calling a new "golden age" for interdisciplinary research.